To solve the problem of decomposing the function \( h(x) = \frac{1}{x^2 + 3x - 10} \) into a composition of two functions \( f \) and \( g \), we need to identify these functions such that \( h(x) = f(g(x)) \). The goal is to express \( h(x) \) in terms of \( f \) and \( g \).

First, we recognize that \( h(x) \) is a fraction, where the denominator can be treated as the inner function \( g(x) \). Thus, we can define:

\( g(x) = x^2 + 3x - 10 \)

Next, the outer function \( f(x) \) will be the operation applied to \( g(x) \). Since \( h(x) \) is the reciprocal of \( g(x) \), we can express \( f(x) \) as:

\( f(x) = \frac{1}{x} \)

Putting it all together, we have:

\( h(x) = f(g(x)) = f(x^2 + 3x - 10) = \frac{1}{x^2 + 3x - 10} \)

This decomposition shows that \( g(x) \) captures the polynomial in the denominator, while \( f(x) \) represents the reciprocal function. This method of decomposition is intuitive and effectively illustrates the relationship between the functions.

In summary, the functions are:

\( g(x) = x^2 + 3x - 10 \)

\( f(x) = \frac{1}{x} \)

By composing these functions, we can reconstruct the original function \( h(x) \). This approach highlights the importance of understanding function composition in algebra.